Toeplitz-based iterative image reconstruction for MRI with correction for magnetic field inhomogeneity

Abstract

In some types of magnetic resonance (MR) imaging, particularly functional brain scans, the conventional Fourier model for the measurements is inaccurate. Magnetic field inhomogeneities, which are caused by imperfect main fields and by magnetic susceptibility variations, induce distortions in images that are reconstructed by conventional Fourier methods. These artifacts hamper the use of functional MR imaging (fMRI) in brain regions near air/tissue interfaces. Recently, iterative methods that combine the conjugate gradient (CG) algorithm with nonuniform FFT (NUFFT) operations have been shown to provide considerably improved image quality relative to the conjugate-phase method. However, for non-Cartesian k-space trajectories, each CG-NUFFT iteration requires numerous k-space interpolations; these are operations that are computationally expensive and poorly suited to fast hardware implementations. This paper proposes a faster iterative approach to field-corrected MR image reconstruction based on the CG algorithm and certain Toeplitz matrices. This CG-Toeplitz approach requires k-space interpolations only for the initial iteration; thereafter, only fast Fourier transforms (FFTs) are required. Simulation results show that the proposed CG-Toeplitz approach produces equivalent image quality as the CG-NUFFT method with significantly reduced computation time.

An efficient gridding reconstruction method for multishot non‐Cartesian imaging with correction of off‐resonance artifacts

“…With the proposed method, the effectiveness and efficiency for ORA correction were not determined by the spatial distribution of the off-resonance frequencies, but rather affected by the sparsity of W(j) and the choice of d (see Theory). This is similar to the cases in the optimized direct estimation methods (14,16,18). As long as d is chosen properly, accurate reconstruction in the regions with abruptly varying field inhomogeneities can be obtained (Fig.…”

“…ORA corrections can be performed either simultaneously when the image reconstruction is being done (10)(11)(12)(13)(14)16,18) or postreconstruction on the uncorrected images (19). Obviously, the former approach would be more attractive than the latter because good image quality can be obtained at no cost of additional time.…”

“…As shown in Fig. 1b and c, the field map consisted of a background having a fixed off-resonance frequency of 50 Hz and two regions in which the off-resonance frequencies varied abruptly from 50 to 100 Hz and from À50 to 50 Hz, respectively, to simulate the two situations of field inhomogeneity frequently encountered in practice (16,18). It was assumed that 3639 data points were acquired, with a readout time of 29.1 ms for each interleaf.…”

Advanced three‐dimensional tailored RF pulse for signal recovery in T2*‐weighted functional magnetic resonance imaging

“…Using the time segmentation (22,24) and frequency segmentation (21,23) methods, reconstruction is sped up significantly via approximations to the frequency offset exponential term in the magnetic resonance signal equation, and the subsequent use of the efficient (NU)FFT algorithm. These segmentation methods, in the context of CG-based reconstruction, have recently been generalized in (28). The analogy between reconstruction and smalltip-angle pulse design suggests that similar segmentation techniques can be applied to accelerate the 3DTRF pulse design process.…”

“…Based on (28), all of the known approximations to the offresonance exponential term in Eq. [5] are special cases of the following general form:…”